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Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 - Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (11,44,2)(6,54,3)
(12,72,3)
(2,32,4)
(7,98,2)
(10,50,5)
(2,32,4)
Identify the relationship: The middle number is obtained by multiplying the first number by the square of the third number.
Identify the relationship: The middle number is obtained by multiplying the first number by the square of the third number.
Analyze the given sets
Given (11, 44, 2): 11 * (2 * 2) = 11 * 4 = 44. Given (6, 54, 3): 6 * (3 * 3) = 6 * 9 = 54. The logic is: Middle Number = First Number * (Third Number squared).
Verify against Option B
Applying the logic to Option B (2, 32, 4): 2 * (4 * 4) = 2 * 16 = 32. This matches the middle number 32, confirming the pattern holds.
A: 12 * (3 squared) = 12 * 9 = 108 (not 72), C: 7 * (2 squared) = 7 * 4 = 28 (not 98), D: 10 * (5 squared) = 10 * 25 = 250 (not 50).
B is correct because the logic applied is that the middle number equals the first number multiplied by the square of the third number, which works only for (2, 32, 4) where 2 * 16 = 32.
When faced with number sets, always test simple powers (squares/cubes) of the third number first, as they are common building blocks for middle-term transformations.
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